If X+Y+Z=0 and XYZ=-1 then prove that: 1/1+x3 +1/1+y3 +1/1+z3
Answers
Answered by
0
Answer:
Given:- xyz=1
To prove:- (1+x+y
−1
)
−1
+(1+y+z
−1
)
−1
+(1+z+x
−1
)
−1
=1
Proof:-
Taking L.H.S.-
(1+x+y
−1
)
−1
+(1+y+z
−1
)
−1
+(1+z+x
−1
)
−1
=(1+x+xz)
−1
+(1+y+xy)
−1
+(1+z+yz)
−1
=(1+x+xz)
−1
+(xyz+y+xy)
−1
+(1+z+yz)
−1
=(1+x+xz)
−1
+y
−1
(1+x+xz)
−1
+(1+z+yz)
−1
=(1+x+xz)
−1
(1+y
−1
)+(1+z+yz)
−1
=(xyz+x+xz)
−1
(1+y
−1
)+(1+z+yz)
−1
=x
−1
(1+z+yz)
−1
(1+y
−1
)+(1+z+yz)
−1
=(1+z+yz)
−1
(x
−1
+(xy)
−1
)+(1+z+yz)
−1
=(1+z+yz)
−1
(yz+z+1)
=
1+z+yz
1+z+yz
=1
If R.H.S IS EQUAL TO 1 THEN AUTOMATICALLY L H.S IS ALSO 1
Similar questions